In 2010, Paramore had it all. They'd gone from emo-teen punk-poppers to stadium-filling rock band whose third album, Brand New Eyes, had shot straight in at No 2 on the Billboard charts. They played the Reading and Leeds festivals, sandwiched at the top of the bill between Blink-182 and Weezer. They had an army of dedicated teen fans who hung on their every blog post, of which there were many. But all was not well. A traumatic split was imminent, and a higher power was behind it.

A brief recap. Paramore got together as teens in Franklin, near Nashville, in 2005. They released two albums in quick succession, moving from the punky garage circuit to bigger rock shows by the time they had turned 18. They caught the crest of the emo wave, but their ear for a melody lifted them above their black-fringe-and-eyeliner contemporaries, and the presence of sparky frontwoman Hayley Williams made them destined for bigger things.

The band were practising Christians – not so common in the rock'n'roll fraternity – but reluctant to define themselves by it. "We are Christians, but we're not a Christian band," guitarist Josh Farro said. Hayley took to Livejournal to agonise over a line from their breakout hit Misery Business, "God does it feel so good", though she refused to proselytise. "You don't have to believe in what I believe and no one in Paramore is ever going to go around forcing our faith into people's lives," she wrote.

As their second album Riot! blew up, tensions inside the band began to erupt. Paramore had been built around the core of Hayley and Josh. They were a couple for much of their early days, but, as with most teen romances, it didn't last. In February 2008, a European tour was suddenly pulled. "There are a lot of internal issues that have been going on in this band for quite a while now," Hayley wrote at the time in a post to fans. "Maybe one day we will tell the whole story but for now, just know that all five of us are going to work so hard to get it right."

It seemed as if everyone in Paramore had been doing some soul-searching. Two weeks prior to the hiatus, Josh had expressed some dissatisfaction about how they were portrayed in the media. "We are a band. It's not just Hayley; it's not her band. Just because she's the lead singer doesn't mean she's the only one involved," he said. Their fans, naturally, begged them not to call it a day, and for a time, they held it together. They quickly recorded 2009's Brand New Eyes, a beefy, slick rock album that solidified their place in the mainstream. Commercially, they became bigger than ever. But it wasn't sustainable. Hayley, by her own admission, had crammed allusions to the failed relationship into the lyrics of Brand New Eyes, but the band, eager to keep working, had kept their heads down and ploughed on.

'We all took turns being pissed, and being the person trying to control that. Like, don't say anything...' Jeremy on the brothers' split

The following year, at the end of summer, Josh and brother Zac told the others they were leaving. Hayley and the remaining members, Taylor York and Jeremy Davis, released a statement: "We want Josh and Zac to do something that makes them happy and, if that isn't here with us, then we support them finding happiness elsewhere."

That was supposed to be the end of it. It wasn't. Out of the blue, Josh posted a 1,500-word blog on his own website that criticised everything from the way the band had been put together to the lyrics of Brand New Eyes, which he deemed ungodly. "For example, 'The truth never set me free', which contradicts what the Bible says in John 8:32 ('and you shall know the truth, and the truth shall sat [sic] you free')." He said "prayer and counsel" had led them to their decision to leave. The post ended, "All of the glory be to God." Hayley, Taylor and Jeremy were stunned.

"It was... disgusting, honestly," says Hayley, with a clear look of dismay. It's two years later, and the band are in London to announce the release of their fourth album, their first as a three-piece. It's called Paramore and is due out in April.

"It was really hard to bite our tongues," says Taylor, who's furiously doodling a turtle with laser eyes and avoiding any eye contact. "We spent so long with them, and we really do love them, it was such a weird feeling of... I don't know. It almost felt like, for that period of time, we didn't know them. We had a lot of negative emotions."

Jeremy admits that they were all tempted to retaliate, but they held each other back: "We all took turns being pissed, and being the person trying to control that. Like, don't say anything..."

When asked if they were always optimistic they could carry on as a three-piece, there's a long pause. Taylor doodles.

"Ummmmmmm," says Hayley. "Not always." Silence.

Taylor looks up: "Honestly, it was just really scary. It felt so overwhelming. We had all of this momentum, and we'd finally got a system, however dysfunctional. And that all went away. It was the best thing that could have possibly happened but at the time it didn't feel like that."

The split is obviously still raw. They talk of "living in denial" promoting Brand New Eyes until, as Hayley puts it, "everything just broke, and the tension was gone". They haven't spoken to the brothers since the offending post. Hayley doesn't know if they ever will again. "I guess right now, I'm so thankful for everything that happened, how could I be angry?" She draws a telling analogy: "Imagine being in a relationship. You get broken up with. You get bummed out. Then you meet the man of your dreams. Are you still going to be an asshole?" She shrugs: "We're happy now, and that's all that matters."

That happiness is manifest on their new album, a huge pop beast full of handclaps and gospel choirs and organs that is more than a little bit mid-90s No Doubt. It's produced by former Beck and Nine Inch Nails bassist Justin Meldal-Johnsen AKA JMJ, last heard pushing the buttons on M83's Hurry Up, We're Dreaming. They went to meet him, thinking he'd be "too cool for our band", but hit it off. While in some ways the record is a departure, it isn't a complete about-face, adding upbeat bells and whistles, and a sense of palpable ambition. One new song, Ain't It Fun, sounds as if Alexander O'Neal has just discovered Refused's back catalogue.

Perhaps this more direct pop feel – you can definitely dance to Ain't It Fun – is a practical choice as much as an artistic one. After all, Paramore had a largely teenage fan base. They were loosely aligned with the likes of Fall Out Boy and Panic! At The Disco, though they always had a more tuneful ear. Now those fans will be in their 20s, as are the band (Jeremy is married; he spends much of the afternoon showing phone videos of his new dog). Things have moved on.

"Emoooo!" shouts Hayley. "I put a picture of this on my Twitter: 'Nobody says emo any more.' I'm going to bring it back!" she jokes.

Jeremy acknowledges they'd considered this: "After we started writing weird stuff like Ain't It Fun, we got nervous. But that was a comfort. We've grown and we don't like the same music we liked, so why would [our fans] not? That idea kept us pushing ourselves."

In the past, with "all the band drama stuff", they wouldn't have been able to make this record. "With five people, it was harder to compromise," Taylor recalls. "This is the first time we've been able to throw out an idea like, 'Dude, it'd be cool to have a gospel choir', and it wouldn't get shot down."

"As I've got older, I've learned I really don't care if something I love is the coolest," says Hayley. "'What are you listening to? 'Uh, the Smiths?' No. Just tell them you're listening to old Shania Twain songs."

PARAMORE, FIVE SONGS TO HEAR …

Misery Business (2007) Their first big hit: a barbed, rousing pop-rock attack on a particularly mean girl.

In The Mourning (2011) A nod to their Nashville roots, this sweet, country-kissed slowie deals with the immediate aftermath of the Farros' departure.

Decode (2008)Paramore and Twilight go together like fangs and carotid arteries, so naturally they contributed to its soundtrack with this one-off single.